arXiv subjects

P. S. Zykov

Publications and source records attributed to P. S. Zykov.

2 recordsLinked to original sources

arXiv2006

A two-point boundary value problem on a Lorentz manifold arising in A. Poltorak's concept of reference frame

In A. Poltorak's concept, the reference frame in General Relativity is a certain manifold equipped with a connection. The question under consideration here is whether it is possible to join two events in the space-time by a time-like geodesic if they are joined by a geodesic of the reference frame connection that has a time-like initial vector. This question is interpreted as whether an event belongs to the proper future of another event in the space-time in case it is so in the reference frame. For reference frames of two special types some geometric conditions are found under which the answer is positive.

gr-qc↗

arXiv2004

Application of the Wavelet Transform with a Piecewise Linear Basis to the Evaluation of the Hankel Transform

A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a basis such that its scalar product with the Bessel function is calculated analytically. The result is represented as a series, with the coefficients strongly depending on the local behavior of the function being transformed. The application of the method is demonstrated by an example illustrated with plots.

math.NA↗